Answer :
To determine the potential energy of the bicycle resting at the top of a hill, we use the formula [tex]\( PE = mgh \)[/tex], where:
- [tex]\( PE \)[/tex] is the potential energy,
- [tex]\( m \)[/tex] is the mass of the object,
- [tex]\( g \)[/tex] is the acceleration due to gravity,
- [tex]\( h \)[/tex] is the height above the reference point.
Given the following values:
- [tex]\( m = 25 \)[/tex] kg (mass of the bicycle),
- [tex]\( g = 9.8 \)[/tex] m/s² (standard gravitational acceleration on Earth),
- [tex]\( h = 3 \)[/tex] m (height of the hill).
Substitute these values into the formula:
[tex]\[ PE = 25 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 3 \, \text{m} \][/tex]
First, multiply the mass ([tex]\( m \)[/tex]) by the gravitational acceleration ([tex]\( g \)[/tex]):
[tex]\[ 25 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 245 \, \text{N (Newtons)} \][/tex]
Next, multiply the result by the height ([tex]\( h \)[/tex]):
[tex]\[ 245 \, \text{N} \times 3 \, \text{m} = 735 \, \text{J (Joules)} \][/tex]
Therefore, the potential energy of the bicycle at the top of the hill is [tex]\( 735 \)[/tex] Joules.
Hence, the correct answer is:
735 J
- [tex]\( PE \)[/tex] is the potential energy,
- [tex]\( m \)[/tex] is the mass of the object,
- [tex]\( g \)[/tex] is the acceleration due to gravity,
- [tex]\( h \)[/tex] is the height above the reference point.
Given the following values:
- [tex]\( m = 25 \)[/tex] kg (mass of the bicycle),
- [tex]\( g = 9.8 \)[/tex] m/s² (standard gravitational acceleration on Earth),
- [tex]\( h = 3 \)[/tex] m (height of the hill).
Substitute these values into the formula:
[tex]\[ PE = 25 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 3 \, \text{m} \][/tex]
First, multiply the mass ([tex]\( m \)[/tex]) by the gravitational acceleration ([tex]\( g \)[/tex]):
[tex]\[ 25 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 245 \, \text{N (Newtons)} \][/tex]
Next, multiply the result by the height ([tex]\( h \)[/tex]):
[tex]\[ 245 \, \text{N} \times 3 \, \text{m} = 735 \, \text{J (Joules)} \][/tex]
Therefore, the potential energy of the bicycle at the top of the hill is [tex]\( 735 \)[/tex] Joules.
Hence, the correct answer is:
735 J
